Answers
The solution set of f(x) > 0 is x ∈ (-2, 8).
What is the set of the function?
To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.
Let's start by finding the domain of the function:
x² - 6x - 16 ≠ 0
We can solve for x by using the quadratic formula:
x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13
So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).
Now let's factor the numerator and denominator of f(x):
f(x) = (x + 10)/[(x - 8)(x + 2)]
The critical points occur where the numerator or denominator of f(x) changes sign.
The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.
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Related Questions
what is 5.25 in fraction form?
Answers
Answer:
To convert 5.25 to a fraction, we can first note that the decimal represents the number 5 units and 25 hundredths. We can write this as:
5.25 = 5 + 0.25
Next, we can convert the decimal 0.25 to a fraction by recognizing that it is equivalent to 25/100 or 1/4. Therefore:
5.25 = 5 + 1/4
We can then combine the whole number 5 with the fraction 1/4 by finding a common denominator:
5 + 1/4 = 20/4 + 1/4 = 21/4
Therefore, 5.25 as a fraction in simplest form is 21/4.
Answer:
i believe it should be
5 1/4
i apologize if wrong, it depends on the ratio (you didnt include it)
A real estate company offered two plans to new employee: plan A is a salary of 2500 per month plus a 6% commission on sales. Plan B is a salary of 3000 per month plus a 4% commission on sales for what amount of monthly sales is plan A better then Plan B
Answers
In Linear equation, The of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
Let x be # sales/month:
Plan A: $2500 + 6%•x
Plab B: $3000 + 4%•x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%•x > $3000 + 4%•x, then solve for x:
2%•x > $500 or x > $500/0.02
x > 25,000
Therefore, the of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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In Linear equation, The of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b.
To solve this system of linear equations, we can use the method of elimination or substitution.
Let x be sales of the month:
Plan A: $2500 + 6% × x
Plan B: $3000 + 4% × x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%×x > $3000 + 4%×x
then solve for x:
=> 2500+0.06x > 3000+0.04x
=> 0.06x-0.04x > 3000-2500
=> 0.02x > 500
=> x > 500/0.02
=> x > 25000
Therefore, the of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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Two students began a proof of the law of sines.
C
b
A
h
Student I
sin(A)
sin(B)
T
bsin(A) = h
asin(B) = h
a
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A) =
sin(B) =
-1/2
asin(A)= h
bsin(B) = h
asin(A)=bsin(B)
sin(A)=sin(B)
B
Which student correctly started the proof, and what should that student do next to complete the proof?
Answers
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Student 1 correctly started the proof.
To complete the proof using the law of sines, student 1 should use the fact that the sum of angles in a triangle is 180 degrees to obtain an expression for angle C, and then use the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side to obtain an expression for side c in terms of sin(A) and sin(B).
Here's the complete proof:
Starting with Student 1's work:
bsin(A) = h
asin(B) = h
Using the fact that the sum of angles in a triangle is 180 degrees:
C = 180 - A - B
Using the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side:
a/sin(A) = b/sin(B) = c/sin(C)
Substituting in the expressions for c and sin(C) in terms of sin(A) and sin(B):
a/sin(A) = b/sin(B) = 2h/(sin(A)+sin(B))
Simplifying:
a = 2hsin(A)/(sin(A)+sin(B))
b = 2hsin(B)/(sin(A)+sin(B))
c = 2hsin(C)/(sin(A)+sin(B)) = 2hsin(180-A-B)/(sin(A)+sin(B)) = 2h*sin(A+B)/(sin(A)+sin(B))
Therefore, the law of sines is:
a/sin(A) = b/sin(B) = c/sin(C) = 2h/(sin(A)+sin(B))
=
Find the value of x.
4route5
8
12
Answers
The value of the missing side x is 12. 6
How to determine the value
We have that the Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides.
From the information given, we have that;
(4√5)² = 8² + y²
find the square values
80 = 64 + y²
collect the like terms
y² = 16
y = 4
Also, using the Pythagorean theorem, we have;
x² = 4² + 12²
find the squares and substitute the values
x² = 16 + 144
x² = 160
Find the square root
x = 12. 6
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What percent of 60 is 63?
Answers
Answer:37.8
Step-by-step explanation:
Answer:
105%
Step-by-step explanation:
First, do 63 x 100 then do 60 x 10 then you get 630 and 600.
Put 630 over 600. 630 / 600 is 1.05, which is converted to 105%
There are 15 Keurig pods in the green basket. It has two Donut Shop, six Swiss Miss hot chocolate, and seven Breakfast Blend flavors. Maddy, Charlie, and Ann like the Donut Shop Keurig pod the best. What is the probability that Ann will get the Donut Shop pod?
Answers
The probability that Ann will get the Donut Shop pod would be = 2/15
How to calculate the probability of getting a Donut Shop pod?The total number of Keurig pods in the green basket = 15
The number of Donut Shop in the basket = 2
Formula for probability;
= possible outcome/sample space
where;
possible outcome = 2
sample space = 15
Probability = 2/15
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Jessica used 2/3 of her money to buy books and 1/6 of her money to buy notebooks. She then had $30 left. How much money did Jessica have before shopping?
Answers
Answer:
Step-by-step explanation:
The total amount of money she spent on books and notebooks is:
2/3x + 1/6x = 5/6*x
Jessica had $30 left, so we can set up an equation:
x - 5/6*x = 30
Simplifying the equation:
1/6*x = 30
x = 180
100 Points! Algebra question. Write a quadratic equation in standard form with -1/2, 3/4 as its roots. Please show as much work as possible. Photo attached. Thank you!
Answers
X^2 -(a+b)x + ab = 0
x^2 -(-1/2 + 3/4)x + (-1)(3)/(2)(4) =0
x^2 -(1/4)x -(3/8) = 0
Evaluate -32 + (2 - 6)(10).
Answer is -49!!!!
Answers
Answer:
-72
Step-by-step explanation:
Because -32 + (2 - 6)(10). is -72
-4 is greater than of equal to x - 11
Answers
Using the inequality rule we know that 11 is greater than -11, (11 > -11).
What is an Inequality Equation?Mathematical expressions with inequalities are those in which the two sides are not equal.
Contrary to equations, we compare two values in inequality.
Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.
So, let's say the inequality equation looks like this: A
Right now, A is valued at
Let p be used to representing the initial number.
P equals 11, so
Let q be used to representing the second number.
Q has a value of -11.
-11 and 11 are both numbers that are greater than zero.
Then, 11 > -11 ... (1)
A has a value of 11 > -11.
Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).
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Correct question:
Is 11 greater than, equal to, or less than -11?
The numbers 1/2,x,y,3/4 are in increasing order of size. The differences between successive numbers in this list are all the same. What is the value of y?
Answers
x - 1/2 = y - x = 3/4 - y
Simplifying each of these equations, we get:
2x - 1 = 2y - 1/2
2y - 1/2 = 3/4 - y
Solving for x in the first equation, we get:
x = y + 1/4
Substituting this into the second equation, we get:
2y - 1/2 = 3/4 - (y + 1/4)
Simplifying this equation, we get:
3y = 1/2
Therefore, y = 1/6.
Let d be the common difference between the numbers. Then we have:
x - 1/2 = d
y - x = d
3/4 - y = d
Adding the first and third equations, we get:
(3/4 - 1/2) + (x - y) = 2d
Simplifying, we have:
1/4 + (x - y) = 2d
Substituting the second equation into this expression, we get:
1/4 + d = 2d
Solving for d, we get:
d = 1/4
Substituting this value of d into the first equation, we get:
x - 1/2 = 1/4
x = 3/4
Substituting this value of x into the second equation, we get:
y - 3/4 = 1/4
y = 1
Therefore, the value of y is 1.
Which of the following equations represents a quadratic function?
a. x=y^2-2y+4
b. y=3x^2-5x+9
c. y=-2x^2+16√x-64
d. -5x+3y=-4
Answers
The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]
What is a quadratic function ?
A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.
In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.
Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.
Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.
Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.
Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.
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Each grid square is 1 square unit. Find the area, in square units, of the shaded region without counting every square. Be prepared to explain your reasoning.
Answers
Answer:
The area of the shaded region is 27 units^2.
Step-by-step explanation:
Area of outer square = 6^2 = 36 units^2
Area of inner square = 3^2 = 9 units^2
Area of shaded region
= 36 units^2 - 9 units^2 = 27 units^2
The area of a shaded region in a unit grid can be found either by subtracting the area of unshaded regions from the total grid area or by adding up the areas of identifiable shapes within the shaded region.
Explanation:To find the area of the shaded region without counting every square, you can use a few different strategies, such as identifying and subtracting the area of unshaded regions from the total grid area, or recognizing and adding together larger, easily countable shapes within the shaded region.
For example, if your grid is 10x10 units, the total area would be 100 square units. If, within that grid, there are 20 unshaded squares, you can subtract this from the total area to find the area of the shaded region. So, 100 total square units - 20 unshaded square units = 80 shaded square units. This approach works best when the number of unshaded squares is relatively small or easily countable.
Alternatively, if the shaded region forms easily identifiable shapes (like a 5x5 square or a 3x10 rectangle), you can add the areas of these shapes together to get the total shaded area. This approach works best when the shaded region forms a few large, simple shapes.
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PLEASE RESPOND FAST I NEED IT ANSWERED
The data set lists the ages of the cast members of a recent children’s play. Find the median age. {14, 11, 8, 12, 5, 3, 17, 10, 8, 11}
Answers
Answer:
Mean: 9.9
Median: 10.5
Step-by-step explanation:
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2548 feet and Plane B is just taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 70.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitude be when they're at the same altitude?
Answers
When they are at the same altitude, the distance between the planes will be 3962 feet.
Why do aircraft go at 30000 feet?Because the air is less dense at high altitudes, planes can fly quicker and consume less fuel. Additionally, at altitudes of 30,000 feet or more, airplanes may steer clear of weather systems, improving the comfort level inside.
What's the maximum altitude an aircraft can travel?The majority of commercial airplanes are permitted to soar as high as 42,000 feet. This upper limit is frequently referred to as a "service ceiling."
The planes will be at the same altitude when t seconds have passed, in which case 25.25t + 2548 = 70.75t,
45.5t = 2548 t = 56 seconds,
and 70.75 * 56 = 3962 feet.
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What is the ratio of yellow to red
6 yellow = 5 green
4 green = 3 purple
5 purple = 2 red
A.3 to 1
B.4 to 1
C.5 to 1
D.6 to 1
Answers
===================================================
Explanation:
We have 5 green in the 1st row and 4 green in the 2nd row.
The LCM is 5*4 = 20.
The ratio [tex]6 \text{ yellow} = 5 \text{ green}[/tex] scales up to [tex]24 \text{ yellow} = 20 \text{ green}[/tex] after multiplying both sides by 4.
The ratio [tex]4 \text{ green} = 3 \text{ purple}[/tex] scales up to [tex]20 \text{ green} = 15 \text{ purple}[/tex] after multiplying both sides by 5.
--------------
These set of ratios
[tex]6 \text{ yellow} = 5 \text{ green}\\\\4 \text{ green} = 3 \text{ purple}\\\\[/tex]
scale up to
[tex]24 \text{ yellow} = 20 \text{ green}\\\\20 \text{ green} = 15 \text{ purple}\\\\[/tex]
The key is the "20 green" on each line. This leads to the ratios linking up.
If A = B and B = C, then A = C (transitive property).
So we can say [tex]24 \text{ yellow} = 20 \text{ green} = 15 \text{ purple}\\\\[/tex]
That simplifies to [tex]24 \text{ yellow} = 15 \text{ purple}\\\\[/tex]
We can divide both sides by 3 to get [tex]8 \text{ yellow} = 5 \text{ purple}\\\\[/tex]
--------------
We now have these set of ratios
[tex]8 \text{ yellow} = 5 \text{ purple}\\\\5 \text{ purple} = 2 \text{ red}\\\\[/tex]
Connect those two equations together to get
[tex]8 \text{ yellow} = 2 \text{ red}\\\\[/tex]
Lastly, divide both sides by 4
[tex]4 \text{ yellow} = 1 \text{ red}\\\\[/tex]
The ratio of yellow to red is 4 to 1.There are 132
chairs in a room.
99 of the chairs are red.
What percentage of the chairs are red?
Answers
Answer:
75%
Step-by-step explanation:
99/132=0.75
Answer:
75% of the chairs are red
Step-by-step explanation:
99/132 chairs are red. When divided, that equals 0.75. 0.75 is equivalent to 75%.
Select the expression that represents this real-world situation.
There are p people on the bus. At the next stop, 8 people get off and 5 more get on. Write an expression to show how many people are on the bus.
p − 8 + 5
p + 8 − 5
p x (8 + 5)
p ÷ (8 − 5)
Answers
The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
What is an expression?An expression is a combination of numbers, symbols, and/or operators that represents a quantity, a value, or a computation. Expressions can include variables, which are letters that represent unknown values, and can be manipulated and evaluated using mathematical operations like addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they are used in various areas of mathematics, including algebra, calculus, and geometry, as well as in many other fields such as physics, engineering, and economics.
According to the given information:The expression that represents the real-world situation is:
p - 8 + 5
Explanation:
Initially, there are p people on the bus. Then, 8 people get off, which is represented by the subtraction of 8 from p (p - 8). After that, 5 more people get on the bus, which is represented by adding 5 to p - 8, giving us the final expression: p - 8 + 5. This expression simplifies to p - 3, which represents the final number of people on the bus.
Therefore, The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
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HELP PLEASE I NEED HELP
Answers
C=(pi)d
Diameter = C/pi
d = 88/pi
d = 20
You can use 3.14 as pi just rounds it up
Brandon used an indoor rock-climbing wall seven times. His climbing times, in
minutes, are shown in this list.
35, 16, 17, 18, 13, 13, 14
Why is the median the most useful measure of central tendency for these
times?
A The median is not affected by an outlier.
B
The median is equal to the range of the data.
C The median is the time that occurs most often.
D The median is a larger.value than the mean of the data.
Answers
The median the most useful measure of central tendency for these
times: is A) The median is not affected by an outlier.
Why is the median the most useful measure?The median is the middle value in a set of data when the values are arranged in order. In this case, the median of Brandon's climbing times would be 16, because it is the fourth value when the times are arranged in order:
13, 13, 14, 16, 17, 18, 35
The median is the most useful measure of central tendency for these times because it is not affected by an outlier, which is a value that is much larger or smaller than the other values in the data set.
In this case, the value 35 is an outlier, because it is much larger than the other values. If we were to use the mean as the measure of central tendency, the outlier would greatly influence the result. However, the median is not influenced by outliers, and therefore provides a better representation of the typical climbing time for Brandon.
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Find the surface area
Answers
I actually do not know because I am still in grade 6
Tim and Ann are both taking the____science course.
Which of these words would indicate that the
course is taught at a faster pace than the
other science courses?
F required
G elective
H condensed
J accelerated
Answers
Answer:
answer is ( J )
Step-by-step explanation:
The word that would indicate that the course is taught at a faster pace than the other science courses is "accelerated." Therefore, the correct answer is J.
What is the equation and solution?
Answers
Answer:
Step-by-step explanation:
x + 5 = 3x - 7
-2x = -12
x = 6
x + 5 = 6 + 5 = 11
3(6) - 7 = 18 - 7 = 11
I'm 2x-3y=-13
4x+2y= -2
Solve ỉn substitute method,Elimination method and Graphical Method
Answers
The value of x and y are -3 and 3 respectively as shown in the graph
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Given the equation:
2x - 3y = -13 (1)
Also:
4x + 2y = -2 (2)
From equation 2:
4x + 2y = -2
2y = -4x - 2
y = -2x - 1
substitute y = -2x - 1 in equation 1:
2x - 3(-2x - 1) = -13
2x + 6x + 3 = -13
8x = -16
x = -2
Put x = -2 in eqn 2:
4(-2) + 2y = -2
-8 + 2y = -2
2y = 6
y = 3
The value of x and y are -3 and 3 respectively
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Simplify (5x4y2)(2x2y).
10x8y2
10x6y3
10x6y2
7x6y3
Answers
Answer:
10*8y2
Step-by-step explanation:
(5*4y2)(2*2y)(5*4y2)(2*2y)5*4y2*2*2y(5*2)(4y2*2y)(10)(8y2)Use the following chart of years and price for an unstated item to answer the following questions.
1970 1975 1980 1985 1990 1995 2000
$87.32 $119.99 $206.79 $264.16 $283.16 $351.94 $349.69
What was the relative change from 1995 to 2000? (Enter your answer as a percentage rounded to the nearest hundredths.)
Answers
The relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
How to calculate the relative change?To calculate the relative change from 1995 to 2000, we need to find the difference between the prices in those two years, and then express that difference as a percentage of the price in 1995.
Price in 1995 = $351.94
Price in 2000 = $349.69
Difference = Price in 2000 - Price in 1995
Difference = $349.69 - $351.94
Difference = -$2.25
The negative sign indicates a decrease in price from 1995 to 2000.
Now, we can calculate the relative change as a percentage:
Relative change = (Difference / Price in 1995) * 100
Relative change = (-$2.25 / $351.94) * 100
Relative change = -0.6392 * 100
Relative change = -63.92%
Therefore, the relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
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Lyle uses 13 cups of shredded cheese to make a large pizza. How many cups of shredded cheese will he use to make 5 pizzas?
Answers
If you multiply 13 times 5, you will get the equivalent of 65. Hence being the answer.
Answer:
65
Step-by-step explanation:
cups per pizza- 13
for 5 pizza- 13×5= 65
think of it this way you eat 2 slices of pizza in an hour, how many will you eat in 6 hours? 2x6 = 12
What is the probability that either event will occur?
15
A
B
12 18
21
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answers
The probability that either event will occur is given as follows:
P(A or B) = 0.83.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The "or probability" is defined as follows:
P(A or B)=P(A) + P(B) - P(A and B).
From the Venn Diagram, the probabilities of each event are given as follows:
P(A) = 18/(18 + 12 + 6) = 0.5.P(B) = 12/(18 + 12 + 6) = 0.3333.P(A and B) = 0 -> no intersecton.Hence the or probability is given as follows:
P(A or B) = 0.5 + 0.3333 + 0
P(A or B) = 0.83. (rounded to the nearest hundredth).
Missing Information
The Venn diagram is given by the image presented at the end of the answer.
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equation of line perpendicular to y = -4x + 3 with point 8, 1
Answers
The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;
Slope, m = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 1/4(x - 8)
y = 1/4(x) - 1
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Rewrite 5/6 with a least common denominator equal to
Answers
5/6 can be rewritten with a least common denominator of 6 as 10/12.
What does Fraction means ?Fracture is part of the whole. A fraction consists of two parts, the numerator and the denominator. Numerator: The numerator represents the number above the fraction bar. For example, for 6/7, 6 is the numerator. Denominator: The denominator shows the number placed under the fraction bar.
We can write 5/6 in the lowest common denominator, we need to find the common multiple of 6. The smallest multiple is 2. So we can write 5/6 with the lowest denominator 6 as follows:
5/6 = (5/6) x (2/2) = 10/12
Therefore, 5/6 can be rewritten as 10/12 with a lowest common denominator of 6.
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